Mixed Bing–Whitehead decompositions
Mixed Bing–Whitehead decompositions
Mixed Bing–Whitehead decompositions are a special class of toroidal decompositions of the 3-sphere, defined as the intersection of infinite nested sequences of solid tori. The Bing decomposition and the Whitehead decomposition from previous chapters are both examples of mixed Bing–Whitehead decompositions. In this chapter a precise criterion for when toroidal decompositions shrink is given, in terms of a ‘disc replicating function’. In the case of mixed Bing–Whitehead decomposition, this measures the relative numbers of Bing and Whitehead doubling in the sequence of solid tori in the definition. Mixed Bing–Whitehead decompositions are related to the boundaries of skyscrapers, and the shrinking theorem proved in this chapter will be key to the eventual proof of the disc embedding theorem.
103-114
Kasprowski, Daniel
44af11b9-4d22-49f2-a6a3-04009f45b075
Kim, Min Hoon
49407dfc-bb75-4c69-9e6a-01cf2242bf7e
20 July 2021
Kasprowski, Daniel
44af11b9-4d22-49f2-a6a3-04009f45b075
Kim, Min Hoon
49407dfc-bb75-4c69-9e6a-01cf2242bf7e
Kasprowski, Daniel and Kim, Min Hoon
(2021)
Mixed Bing–Whitehead decompositions.
In,
Behrens, Stefan, Kalmar, Boldizsar, Kim, Min Hoon, Powell, Mark and Ray, Arunima
(eds.)
The Disc Embedding Theorem.
Oxford University Press, .
(doi:10.1093/oso/9780198841319.003.0008).
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Abstract
Mixed Bing–Whitehead decompositions are a special class of toroidal decompositions of the 3-sphere, defined as the intersection of infinite nested sequences of solid tori. The Bing decomposition and the Whitehead decomposition from previous chapters are both examples of mixed Bing–Whitehead decompositions. In this chapter a precise criterion for when toroidal decompositions shrink is given, in terms of a ‘disc replicating function’. In the case of mixed Bing–Whitehead decomposition, this measures the relative numbers of Bing and Whitehead doubling in the sequence of solid tori in the definition. Mixed Bing–Whitehead decompositions are related to the boundaries of skyscrapers, and the shrinking theorem proved in this chapter will be key to the eventual proof of the disc embedding theorem.
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Published date: 20 July 2021
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Local EPrints ID: 475482
URI: http://eprints.soton.ac.uk/id/eprint/475482
PURE UUID: c7275fe4-dc60-400e-b659-704b563a64d9
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Date deposited: 20 Mar 2023 17:41
Last modified: 13 Sep 2024 02:08
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Contributors
Author:
Daniel Kasprowski
Author:
Min Hoon Kim
Editor:
Stefan Behrens
Editor:
Boldizsar Kalmar
Editor:
Min Hoon Kim
Editor:
Mark Powell
Editor:
Arunima Ray
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